Dynamic measurements of transverse optical trapping force in biological applications

Optical tweezers present a technology for measurements of biological forces in the piconewton range. In such applications, one method of calibrating the transverse optical trapping force involves relating a known external force to the displacement of the trapped object from the trapping center. In this work we used Fourier analysis of the equation of motion to calculate the displacement of the trapped object from the trapping center under an external force induced by viscous drag. Triangular waveforms of different frequencies were used both in theoretical modeling and experiments to induce a force on a trapped object. We investigated the contribution of various factors including frequency of the external force, fluid viscosity, density, and dimensions of the trapped object, stiffness of the optical trap, and frequency response of the instruments used to control the motion of the viscous medium to the accuracy of the calibration. The developed model can be adopted for calibration of the transverse trapping force, analysis of the trapped object motion, and reconstruction of a force profile during measurements of dynamic biological forces.